Question

Which expression is equivalent to 2x2 – 2x + 7?

Answer 1

Assuming 2x2 means 2x^2, complete the square:

2x^2 − 2x + 7
= 2(x^2 − x) + 7
= 2[(x − 1/2)^2 − 1/4] + 7
= 2(x − 1/2)^2 + 13/2.

So an equivalent expression is 2(x − 1/2)^2 + 13/2.